PCA Tomography and its application to nearby galactic nuclei

João Steiner

IAG - Universidade de São Paulo

+R. B. Menezes, T. V. Ricci

+F. Ferrari (UNIPAMPA)

Principal Component Analysis - PCA

• Data cubes have huge number of pixels (6 x 106). How can we extract information?

• PCA tomography:• Not a set of objects; a set of spatial pixels of the same

data cube. The wavelength pixels are the properties.• Linear transformation to a new system of coordinates• The coordinates are orthogonal• Dimensional reduction• A lot of redundancy!• Noise reduction – background subtraction• Data organization and analysis

From a datacube to a data matrix

• The datacube has n = x spatial pixels and m spectral pixels.

• The mean intensity

• The intensity adjusted

• The data cube Iij has to be transformed into a matrix, Iβλ

were β = μ(i-1) + j

1 1

1

i jOijIn

Q

QIIOijij

PCA – Principal Component Analysis

• Covariance matrix

• Properties

• PCA transformation:

• D must be diagonal:The diagonal elements of D are the

eigen-values Λk

1cov

n

IIC

T

TCC covcov

kk EIT

1cov

n

TTD k

Tk

Eigen-spectra and Tomograms

• Eλk are the eigen-spectra

and, (transforming β into ij)

• Tijk are the tomograms

Analysing both together may reveal a wealth of information!

• Λk are the eigenvalues

Reconstruction, Compression Cosmetics

• Reconstructing the datacube with relevant eigenvectors to k=r.

• Callibrating flux back

• Noise may be evaluated as

Tkk rErTrI )()('

QrIrI ijOij )(')('

mk

rkk

1

2

NGC 4736 (5 Mpc)GMOS – IFU

NGC 4736 – Gemini 8m x Palomar 5m No AGN LINER

6200 6300 6400 6500 6600 6700 6800

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Flu

x (

10

-15 e

rg/c

m2 .s.A

)

Wavelength (A)

Eigenvalues and variance explained(Huge redundancy)

Tomogram 1 and eigenspectrum 1

Tomogram 2 and eigenspectrum 2

Tomogram 3 and eigenspectrum 3

The “scree test”

Tomogram 1 (green) + 2 (yellow)

The stellar bulge and the BLR

NGC 7097 (E; 30 Mpc) - GMOS IFU data

1 99.5256

2 0.3849

3 0.0464

4 0.0212

5 0.0059

6 0.0046

7 0.0038

8 0.0012

9 0.0009

10 0.0008

Eigenvector Variance (%)

Scree test – Indicates that untilEigenvector 8 we have usefulresults

NGC 7097: Eigenvector 1 (99.52%):

Mainly the galaxy Bulge

NGC 7097: Eigenvector 2 (0.38%):

LINER signature. Red component correlated with the emission line features. Interstellar gas (Na I) in the line of sight to the AGN.

NGC 7097: Eigenvector 3 (0.046%):

Positive correlation is the red component of the line features.Negative correlation is the blue component of the line features.Rotating gaseous disc.

NGC 7097: Eigenvector 4 (0.021%):

A second LINER, but bluer than the one found in Eigenvector 2and displaced 0.15’’ eastward. Absence of Na I absorption.

Same redshift as the first one.

NGC 7097: Eigenvector 5 (0.0059%):

• The central component of the emission line features is anti-correlatedwith their blue and red components. • Ionization cone (correlated) and rotating disc (anti-correlated).

• The LINER is viewed directly through the disc, reddened by dust.• The same LINER is reflected by the clouds in the ionization cone.• We predict that the blue component has polkarized light polarized.

NGC 4151 NIFS data (Storchi-Bergmann et al 2009)

-Re-sample the data to a pixel of 0.021”-Butterworth filter in Fourier space to remove high spatial frequencies-Tomogram 1 can be used as a reliable PSF of the AGN (point source)-It can be used to deconvolve the data cube-Strehl ratio before deconvolution = 0.05-Strehal ratio after deconvolution = 0.15

Feature supression and enhancement

• Defining an object “A”:

• Cube with enhanced feature:

• Or directly

0;1)( Ak

k

kijij AkIAI )()(')('

Tkk ETAI )('

NGC 4151-NIFS observations (Storchi-Bergmann et al 2009)

“software coronagraph”Br γ after switching-off PC1+PC2 HST observations

NGC 4151 – NIFS observations (Storchi-Bergmann et al 2009)

H2 lines – after switching-off PC1+PC2

NGC 1399GMOS IFUInstrument “fingerprint”

T1 T2 T3 T4 T5 T6 T7 T8……. W0

W1

W2

W3

W4

WC

E1 E2 E3 E4 E5 E6 ……….

W0

W1

W2

W3

W4

WC

Steiner et al (2009) MNRAS 395, 64

Relevant software can be found atWWW.astro.iag.usp.br/~pcatomography